Assessment of Stochastic Programming Models for Managing International Bond Portfolios
by
Hercules Vladimirou
Department of Public and Business Administration, University of Cyprus
Coauthors: Stavros Zenios, Charalambos Charalambous

This study concerns the development and empirical evaluation of stochastic programming models for managing bond portfolios in international settings. The models address the total risk exposure of portfolios stemming from interest rate risk in each market and from currency exchange risk across markets. Portfolio risks are considered in an integrated simulation and optimization framework. The Monte Carlo simulation procedure introduced by Consiglio and Zenios [1,2] is extended so as to generate scenario trees that postulate jointly interest rate paths in each market and exchange rates between currencies, thereby prescribing discrete distri butions of holding period returns for the international bonds in a multiperiod setting. The simulation procedure is calibrated based on historical observations that include term structures of interest rates and their volatilities in each market, as well a s their correlations to currency exchange rates. Interest rate paths in each market are sampled from binomial lattice structures on which the underlying securities are priced; these are combined with exchange rate scenarios sampled in conformity with historical correlations.

The joint interest rate and exchange rate scenarios constitute the primary data inputs in stochastic programming models for portfolio management. Two-stage stochastic programming models are examined and compared against myopic (single-period) models. Empi rical tests involving government bonds in the US, German and Swiss markets over the period 01/1997-07/1998 revealed that myopic stochastic programs often attain only marginal improvements in performance over corresponding deterministic mean value models.

Conversely, the expected value of perfect information remains at considerable levels in these models. These observations point to the potential for performance improvements with models that can capture more effectively the underlying uncertainties and the ir dynamic structure in the portfolio management problems, leading naturally to the consideration of two-stage stochastic programming models. The optimization models determine positions in international bonds, thereby resolving in a common framework the interrelated issues of asset allocation among different markets and the specific bond-picking decisions. Comparisons of alternative models consider various dimensions of portfolio performance. Ex-ante measures include the value of the stochastic solution, the expected value of perfect information and descriptive statistics of portfolio return distributions under postulated scenario samples.

Backtesting of the models in a rolling horizon fashion provides a more effective basis for model validation. Ex-post performance measures determined by the backtesting include: attained growth rates and volatilities in portfolio value, effectiveness in tracking a composite index of international bonds, level of diversification, portfolio turnover, and incured transaction costs.

References: [1] A. Beltratti, A. Consiglio, and S.A. Zenios, "Scenario modeling for the management of international bond portfolios", Annals of Operations Research (forthcoming).

[2] A. Consiglio, S.A. Zenios, "Integrated Simulation and Optimization Models for Tracking International Fixed Income Indices", Technical Report 98-05, Dept. of Public and Business Administration, University of Cyprus, Nicosia, Cyprus.

Date received: February 17, 1999

Copyright © 1999 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cacq-12.